Hawkeye Observations of the Shape of the Magnetopause in the Vicinity of the Polar Cusp

X. -W. Zhou and C. T. Russell
Institute of Geophysics and Planetary Physics
University of California, Los Angeles

Introduction

Despite the launch of two early missions HEOS 2 and Hawkeye into highly elliptical polar orbits, we know very little about the solar wind interface with the polar cusp. In this paper we will use Hawkeye data to determine the shape of the magnetopause at high latitudes in an attempt to understand some of the basic physics in this region. Our present lack of understanding is underscored by the stark difference between "vacuum" models of the magnetosphere and MHD simulations. Vacuum models, such as the model of Tsyganenko (1989) of a dipole field in an ellipsoidal superconducting shell, have a polar cusp that is tilted well forward of the terminator except for large tilts of the dipole away from the sun. This is illustrated in Figure 1a, Figure 1b and Figure 1c for tilt angles of 0 degrees, 10 degrees and 30 degrees. However, many MHD models have a cusp that is tilted away from the sun. Examples of such cusps are shown in Figures 2a, 2b (Wu, 1984) while Figure 2c shows a more classical model. The difference between these two types of models may be due to the presence of plasma in the MHD models and its ability to diffuse across the magnetopause due to the finite diffusivity of the codes. An initial study of the shape of the magnetopause below the cusp was attempted using the lower latitude ISEE data by Petrinec and Russell (1995). By examining the shape of the boundary as a function of the latitudinal distance from the cusp as measured by the sum of the tilt angle plus the magnetic latitude of the observation, they found evidence for the indentation of the cusp at high latitudes. This is shown in Figure 3 that compares the observations as plus sign, the fit to these points as a solid line and the model of Spreiter and Briggs [1961] as a dashed line. The observations are clearly consistent with the shape obtained from the Spreiter and Briggs model. The Hawkeye data allows us to make a simple test as to which of these models is closest to the configuration of the terrestrial cusps.

Data Analysis

We have examined time series of the magnetic field data at 46 second resolution for the period June 4, 1974 to June 1, 1976. As shown in Figure 4a and Figure 4b we have identified the magnetopause through its signature in the 3 vector components of the field and in the angles declination D=tan-1[by/(Rxbz- Rzbx)] and inclination I=cos(Rxbx+Rzbz)-90 degrees. Where R is the unit vector from the center of the earth to the point of observation in the Dipole Meridian system, and b is the direction of the magnetic field in the same system. The field values just inside the magnetopause tell us whether the spacecraft is above the cusp or below the cusp. Below the cusp the field lines point away from the sun and above it toward the sun. Figure 4a shows an example of measurements below the cusp and Figure 4b shows an example of measurements above the cusp. Unless we are in the cusp itself we do not know where it is exactly since we can determine whether we are above or below the cusp we can determine where the cusp is statistically. Since we expect that the direction of the IMF will affect the cusp location we examine only magnetopause crossings for which there are IMF measurements on the IMP-8 spacecraft. Figure 5a and b show the location of the magnetopause crossings for magnetopause clock angles within 22.5 degrees of the noon-midnight meridian for north and south IMF respectively. Solid circles show measurements above the cusp and open circles below the cusp. All locations have been normalized by the sixth root of the dynamic pressure to a common 2nPa pressure.

Effect of Dipole Tilt

While Figure 5a, Figure 5b show statistically where the cusp is found, it provides little insight into the dependence of the cusp location or dipole tilt angle or even what the tilt angle was during this period. Figure 6a, Figure 6b, Figure 6c, Figure 6d break up Figures 5a and b into IMF north and south and into three tilt angle ranges <-10 degrees, -10 degrees to 10 degrees, >10 degrees. The median tilt angle is shown in the Figure as well as being illustrated by a tilted arrow. The polar cusp will be encountered polarward of the below the cusp crossings and equatorward of the above the cusp crossings. We see that as the dipole tilts further and further toward the sun the cusp location moves equatorward for both northward and southward IMF. We can quantify this by putting limits on the cusp location for each of our dipole tilt ranges and comparing with the cusp position in the Tsyganenko (1989) vacuum model. Figure 7a and Figure 7b show this for northward and southward IMF separately. In this figure we include positions near the noon-midnight meridian (positional clock angles <22.5 degrees from noon) as well as clock angles further from the noon-midnight meridian (67.5 degrees to 22.5 degrees ) labled "mid" in Figure 7. Clearly the polar cusp is swept back from the vacuum location by the interaction for both IMF northward and southward but somewhat less for the southward orientation. Moreover the sweep back seems to be substantially less than that predicted by Wu.

The 3D Shape of the Magnetopause

Even though we used all the Hawkeye data available to us there is still not enough data to explore the funnel of the polar cusp. Moreover it seems to move. This motion is controlled by more than just the tilt angle of the dipole. The IMF clearly plays a role as may other solar wind parameters. Thus we will not be able to test the assertion of Petrinec and Russell (1995) that lower latitude ISEE data indicate the presence of a cusp. However, we do have enough data to determine the zeroth order shape averaged over any cusp indentation. This average shape is shown in Figure 8a and Figure 8b for three clock angle ranges. The noon midnight meridian ( 22.5 degrees), mid latitudes (22.5 degrees 67.5 degrees) and equatorial (Petrinec et al., 1991). Perhaps surprisingly the equatorial cross-section is larger than the cross-section over the pole for Bz>0. This may be due to the presence of hot plasma in the closed magnetosphere with pressure approaching that of the magnetic field with a near absence of plasma in the tail lobes above the pole cusp. However, for Bz<0 the shapes are all very similar.

Conclusions

Observations with the Hawkeye spacecraft in the neighborhood of the polar cusp show that:

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Last modified: June 23, 1995